Researchers Show New Strategy for Detecting Non-Conformist Particles Called
Anyons

By observing how strange particles called anyons dissipate heat, researchers
have shown that they can probe the properties of these particles in systems
that could be relevant for topological quantum computing.

A team of Brown University researchers has shown a new method of probing the
properties of anyons, strange quasiparticles that could be useful in future
quantum computers.

In research published in the journal Physical Review Letters, the team
describes a means of probing anyons by measuring subtle properties of the
way in which they conduct heat. Whereas other methods probe these particles
using electrical charge, this new method enables researchers to probe anyons
even in non-conducting materials. That’s critical, the researchers say,
because non-conducting systems have far less stringent temperature
requirements, making them a more practical option for quantum computing.

“We have beautiful ways of probing anyons using charge, but the question has
been how do you detect them in the insulating systems that would be useful
in what’s known as topological quantum computing,” said Dima Feldman, a
physics professor at Brown and study co-author. “We show that it can be done
using heat conductance. Essentially, this is a universal test for anyons
that works in any state of matter.”

Anyons are of interest because they don’t follow the same rules as particles
in the everyday, three-dimensional world. In three dimensions, there are
only two broad kinds of particles: bosons and fermions. Bosons follow what’s
known as Bose-Einstein statistics, while fermions follow Fermi-Dirac
statistics. Generally speaking, those different sets of statistical rules
mean that if one boson orbits around another in a quantum system, the
particle’s wave function — the equation that fully describes its quantum
state — does not change. On the other hand, if a fermion orbits around
another fermion, the phase value of its wave function flips from a positive
integer to a negative integer. If it orbits again, the wave function returns
to its original state.

Anyons, which emerge only in systems that are confined to two dimensions,
don’t follow either rule. When one anyon orbits another, its wave function
changes by some fraction of an integer. And another orbit does not
necessarily restore the original value of the wave function. Instead, it has
a new value — almost as if the particle maintains a “memory” of its
interactions with the other particle even though it ended up back where it
started.

That memory of past interactions can be used to encode information in a
robust way, which is why the particles are interesting tools for quantum
computing. Quantum computers promise to perform certain types of
calculations that are virtually impossible for today’s computers. A quantum
computer using anyons — known as a topological quantum computer — has the
potential to operate without elaborate error correction, which is a major
stumbling block in the quest for usable quantum computers.

But using anyons for computing requires first being able to identify these
particles by probing their quantum statistics. Last year, researchers did
that for the first time using a technique known as charge interferometry.
Essentially, anyons are spun around each other, causing their wave functions
to interfere with each other occasionally. The pattern of interference
reveals the particles’ quantum statistics. That technique of probing anyons
using charge works beautifully in systems that conduct electricity, the
researchers say, but it can’t be used to probe anyons in non-conducting
systems. And non-conducting systems have the potential to be useful at
higher temperatures than conducting systems, which need to be near absolute
zero. That makes them a more practical option of topological quantum
computing.

For this new research, Feldman, who in 2017 was part of a team that
measured the heat conductance of anyons for the first time, collaborated
with Brown graduate student Zezhu Wei and Vesna Mitrovic, a Brown physics
professor and experimentalist. Wei, Feldman and Mitrovic showed that
comparing properties of heat conductance in two-dimensional solids etched in
very specific geometries could reveal the statistics of the anyons in those
systems.

“Any difference in the heat conductance in the two geometries would be
smoking gun evidence of fractional statistics,” Mitrovic said. “What this
study does is show exactly how people should set up experiments in their
labs to test for these strange statistics.”

Ultimately, the researchers hope the study is a step toward understanding
whether the strange behavior of anyons can indeed be harnessed for
topological quantum computing.

## Reference:

Thermal Interferometry of Anyons in Spin Liquids by Zezhu Wei, V. F.
Mitrović and D. E. Feldman, 11 October 2021, Physical Review Letters.

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